For this you have follow some steps. And go through following below.
1.You connection string will not write directly inside your code.
For that you have to write your connection string inside a notepad.
And then read the notepad text by streamreader . get connectionstring from your given notepad.
then pass this connectionstring to connect database.
2. Now you will install some another system. You just put that notepad your specific folder or filepath.
...
Indirectly you need connectionstring in dynamic.
Or you can do also
Make a page. On it's page load it will check that connectionstring file exists on that fixed location or not.
If file not exists then it will ask to enter ConnectionString on the start of application.
If file not exit then it will create a file there and write your connection string.
If file exist and connecitonstring exists then your first connectionstring asking page will not display.......